Stochastic Dynamic Behavior Of Several Classes Stochastic Chemostat Models

In this article,we investigate the stochastic dynamic behavior of two classes of stochastic competitive chemostat models and one kind of stochastic food chain chemostat model with variable yields.The article includes five chapters.In Chapter 1,we introduce the research background and main work of this article and some important basic knowledge used in this paper.In Chapter 2,a stochastic competition chemostat model with inhibitor and variable yields is considered.The inhibitor has the dual influences on microorganisems.It not only controls harmful microorganisms but also boosts the beneficial microorganisms(target microorganisms).First,a unique global positive solution for the stochastic model is given.Second,by employing stochastic Lyapunov functions,Ito formula,strong law of large number and some other important inequalities,stochastic characteristics,which including the extinction,the competitive exclusion and the stationary distribution of the microorganisms,for the stochastic competition chemostat model are studied.Moreover,the optimization problem,which is the maximal production of the benefical microorganisms under the minimal inbibitor in finite time,is studied for the stochastic chemostat model.Finally,some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields between plasmid and plasmid free microorganisms in chemostat is discussed.Firstly,it is proved that the stochastic system has a unique global positive solution.Secondly,by using stochason the microorganisms.In Chapter 3,the stochastic competition model tic Lyapunov function,It(?) formula,strong law of large numbers and important inequalities,the asymptotic behavior of the solution of the stochastic competitive chemostat model is studied.In Chapter 4,we investigated the stationary distribution of a stochastic food chain chemostat model with variable yields.It is proved that the stochastic model has a unique global positive solution.Secondly,by using appropriate Lyapunov function,Ito formula,Khasminskii theorem and some important inequalities,the existence of unique ergodic stationary distribution for stochastic food chain chemostat model is studied.Finally,the theoretical results of this chapter are verified by numerical simulation,and the influence of variable yields on the growth of microorganisms and bacteria is shown.In Chapter 5,the content of this paper is summarized and the future research work is prospected.